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Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. (English) Zbl 0542.76093

See the preview in Zbl 0535.76074.

MSC:

76N15 Gas dynamics (general theory)
76L05 Shock waves and blast waves in fluid mechanics
76M99 Basic methods in fluid mechanics

Citations:

Zbl 0535.76074
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References:

[1] Anucina, N.N., Some difference schemes for hyperbolic systems, (), 1-13
[2] Baker, A.J., Research on numerical algorithms for the three-dimensional Navier-Stokes equations, I. accuracy, convergence and efficiency, ()
[3] Baker, A.J.; Soliman, M.O., On the utility of finite element theory for computational fluid dynamics, () · Zbl 0513.76069
[4] Beam, R.M.; Warming, R.F.; Yee, H.C., Stability analysis of numerical boundary conditions and implicit difference approximations for hyperbolic equations, () · Zbl 0488.65039
[5] Brooks, A.; Hughes, T.J.R., Streamline upwind/Petrov-Galerkin methods for advection dominated flow, () · Zbl 0423.76067
[6] Brooks, A.; Hughes, T.J.R., Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput. meths. appl. mech. engrg., 32, 199-259, (1982) · Zbl 0497.76041
[7] Buning, P.G.; Steger, J.L., Solution of the two-dimensional Euler equations with generalized coordinate transformation using flux vector splitting, AIAA-82-0971 AIAA/ASME 3rd joint thermophysics, ()
[8] Caughey, D.A.; Jameson, A., Numerical calculation of transonic potential flow about wing-body combinations, Aiaa j., 17, 175-181, (1979) · Zbl 0392.76047
[9] Christie, I.; Griffiths, D.F.; Mitchell, A.R.; Sanz-Serna, J.M., Product approximation for non-linear problems in the finite element method, IMA J. numer. anal., 1, 253-266, (1981) · Zbl 0469.65072
[10] M. Cohen, Private communication, 1982.
[11] Donéa, J., Finite element analysis of transient dynamic fluid-structure interaction, (), 255-290
[12] Dukowicz, J.K.; Ramshaw, J.D., Tensor viscosity method for convection in numerical fluid dynamics, J. comput. phys., 32, 71-79, (1979) · Zbl 0408.76001
[13] Ecer, A.; Akay, H.U., A finite element formulation of Euler equations for the solution of steady transonic flows, () · Zbl 0515.76064
[14] Engquist, B.; Osher, S., One-sided difference schemes and transonic flow, (), 3071-3074 · Zbl 0432.76052
[15] Fletcher, C.A.J., The group finite element formulation, Comput. meths. appl. mech. engrg., 37, 2, 225-244, (1983) · Zbl 0551.76012
[16] Fried, I.; Malkus, D.S., Finite element mass matrix lumping by numerical integration with no convergence rate loss, Internat. J. solids and structures, 11, 461-465, (1975) · Zbl 0301.65010
[17] Goorjian, P.M.; Van Buskirk, R., Implicit calculations of transonic flows using monotone methods, ()
[18] Goudreau, G.L.; Hallquist, J.O., Recent developments in large scale finite element Lagrangian hydrocode technology, Comput. meths. appl. mech. engrg., 33, 725-757, (1982) · Zbl 0493.73072
[19] Harten, A., The artificial compression method for computation of shocks and contact discontinuities: I. single conservation laws, Comm. pure appl. math., XXX, 611-638, (1977) · Zbl 0343.76023
[20] Harten, A., The artificial compression method for computation of shocks and contact discontinuities: III. self-adjusting hybrid schemes, Math. comput., 32, 142, 363-389, (1978) · Zbl 0409.76057
[21] Harten, A., High resolution schemes for hyperbolic conservation laws, J. comput. phys., 49, 357-393, (1983) · Zbl 0565.65050
[22] Harten, A.; Hyman, J.M.; Lax, P.D., On finite difference approximations and entropy conditions for shocks, Comm. pure appl. math., XXIX, 297-322, (1976) · Zbl 0351.76070
[23] Hughes, T.J.R., A study of the one-dimensional theory of arterial pulse propagation, ()
[24] Hughes, T.J.R., Implicit-explicit finite element techniques for symmetric and non-symmetric systems, (), 255-267
[25] Hughes, T.J.R., Analysis of transient algorithms with particular reference to stability behavior, (), Chapter 2. · Zbl 0547.73070
[26] Hughes, T.J.R.; Brooks, A., A multidimensional upwind scheme with no crosswind diffusion, () · Zbl 0423.76067
[27] Hughes, T.J.R.; Brooks, A., Galerkin/upwind finite element mesh partitions in fluid mechanics, (), 103-112
[28] Hughes, T.J.R.; Brooks, A., A theoretical framework for Petrov-Galerkin methods with discontinuous weighting functions: application to the streamline upwind procedure, () · Zbl 0423.76067
[29] Hughes, T.J.R.; Levit, I.; Winget, J., Unconditionally stable element-by-element implicit algorithm for heat conduction analysis, J. engrg. mech., ASCE, 109, 2, 576-585, (1983)
[30] Hughes, T.J.R.; Levit, I.; Winget, J., An element-by-element solution algorithm for problems of structural and solid mechanics, Comput. meths. appl. mech. engrg., 36, 2, 241-254, (1983) · Zbl 0487.73083
[31] Hughes, T.J.R.; Liu, W.K., Implicit-explicit finite elements in transient analysis: stability theory, J. appl. mech., 45, 371-374, (1978) · Zbl 0392.73076
[32] Hughes, T.J.R.; Liu, W.K., Implicit-explicit finite elements in transient analysis: implementation and numerical examples, J. appl. mech., 45, 374-378, (1978) · Zbl 0392.73077
[33] Hughes, T.J.R.; Pister, K.S.; Taylor, R.L., Implicit-explicit finite elements in nonlinear transient analysis, Comput. meths. appl. mech. engrg., 17/18, 159-182, (1979) · Zbl 0413.73074
[34] Hughes, T.J.R.; Winget, J.; Levit, I.; Tezduyar, T.E., New alternating direction procedures in finite element analysis based upon EBE approximate factorizations, (), 75-109 · Zbl 0563.73052
[35] Johnson, C., Finite element methods for convection-diffusion problems, () · Zbl 0505.76099
[36] Kelly, D.W.; Nakazawa, S.; Zienkiewicz, O.C.; Heinrich, J.C., A note on upwinding and anisotropic balancing dissipation in finite element approximations to convective diffusion problems, Internat. J. numer. meths. engrg., 15, 1705-1711, (1980) · Zbl 0452.76068
[37] Lax, P.D., Weak solutions of nonlinear hyperbolic equations and their numerical computation, Comm. pure appl. math., 7, 159-193, (1954) · Zbl 0055.19404
[38] Lax, P.D., Hyperbolic systems of conservation laws II, Comm. pure appl. math., 10, 537-566, (1957) · Zbl 0081.08803
[39] Lax, P.D., Nonlinear hyperbolic systems of conservation laws, () · Zbl 0108.28203
[40] Liepmann, H.W.; Roshko, A., Elements of gasdynamics, (1957), Wiley New York · Zbl 0078.39901
[41] Lomax, H.; Martin, E.D., Fast direct numerical solution of the nonhomogenous Cauchy-Riemann equations, J. comput. phys., 15, 1, 55-80, (1974) · Zbl 0294.65053
[42] H. Lomax et al., Private communications, 1981-1982.
[43] Moretti, G., A physical approach to the numerical treatment of boundaries in gas dynamics, ()
[44] Morton, K.W., Shock capturing, Fitting and recovery, department of mathematics, (1982), University of Reading
[45] Nakazawa, S., Finite element analysis applied to polymer processing, ()
[46] Nävert, U., A finite element method for convection-diffusion problems, ()
[47] Osher, S., Approximation par éléments finis avec décentrage pour des lois de conservation hyperboliques non linéaires multi-dimensionelles, C.R. acad. sci. Paris, Sér., A290, 819-821, (1980) · Zbl 0457.65072
[48] Osher, S., Approximation par elements finis avec decentrage de problemes de perturbations singulières quasi linéaries et multidimensionnels, C.R. acad. sci. Paris, Sér., 1292, 99-101, (1981) · Zbl 0471.65070
[49] Osher, S., Nonlinear singular perturbation problems and one sided difference schemes, SIAM J. numer. anal., 18, 129-144, (1981) · Zbl 0471.65069
[50] Osher, S., Numerical solution of singular perturbation problems and hyperbolic systems of conservation laws, () · Zbl 0457.76035
[51] Osher, S., Shock modelling in aeronautics, () · Zbl 0529.76058
[52] Raymond, W.H.; Garder, A., Selective damping in a Galerkin method for solving wave problems with variable grids, Monthly weather rev., 104, 1583-1590, (1976)
[53] Salas, M.D., Recent developments in transonic Euler flow over a circular cylinder, ()
[54] Spradley, L.W.; Stalnaker, J.F.; Ratliff, A.W., Computation of three-dimensional viscous flows with the Navier-Stokes equations, ()
[55] Steger, J.L., Implicit finite difference simulation of flow about arbitrary geometries with application to airfoils, AIAA paper 77-665, (1977)
[56] Steger, J.L., A preliminary study of relaxation methods for the inviscid conservative gasdynamics equations using flux splitting, NASA contractor rept. 3415, (1981)
[57] Steger, J.L.; Warming, R.F., Flux vector splitting of the inviscid gasdynamics equations with application to finite difference methods, J. comput. phys., 40, 2, 263-293, (1981) · Zbl 0468.76066
[58] Thomasset, F., Implementation of finite element methods for Navier-Stokes equations, (1981), Springer New York · Zbl 0475.76036
[59] Turkel, E., Symmetrization of the fluid dynamic matrices with applications, Math. comput., 27, 124, 729-736, (1973) · Zbl 0298.65064
[60] Warming, R.F.; Beam, R.M.; Hyett, B.J., Diagonalization and simultaneous symmetrization of the gas-dynamic matrices, Math. comput., 29, 132, 1037-1045, (1975) · Zbl 0313.65084
[61] Warming, R.F.; Beam, R.M., On the construction and application of implicit factored schemes for conservation laws, () · Zbl 0392.65038
[62] Weinberger, H.F., A first course in partial differential equations, (1965), Ginn Waltham MA · Zbl 0127.04805
[63] Wilkins, M.L., Calculation of elastic-plastic flows, Lawrence livermore laboratory, rept. UCRL-7322, (1969), Rev. 1, Livermore, CA
[64] Yee, B.C., Numerical approximation of boundary conditions with applications to inviscid equations of gas dynamics, Nasa tm 81265, (1981)
[65] Zienkiewicz, O.C., The finite element method, (1977), McGraw-Hill London · Zbl 0435.73072
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